The advantage of (REF ) is that it is an unconstrained problem that, provided we have enough samples and the parametrization is rich enough, can approximate the constrained statistical problem ( REF ). Namely, the difference between the optimal value of the empirical dual \(D^{\star }_{\text{emp}}\)  and the statistical primal \(P^{\star }\) , i.e., the empirical duality gap is bounded [1]}.
